The Tunnel was a dramatic account of the Battle of the Crater. While the production took a few liberties for dramatic purposes, it was essentially a fair & accurate depiction of history. For example, I remember that in "The Tunnel", Burnside did not provide ladders for his troops climb out of their trenches. The historical fact may well be that it was the case for both the Union trenches and the Crater itself but it was only emphasised as the troops left their trenches. The Wikipaedia Article indicates that the Union forces had exited their trenches and assembled behind their lines to await the explosion. When that moment came, they were supposed to cross over their trenches on specially made "bridges" and charge towards the Crater. None of these special bridges were ever constructed and/or deployed so the advancing Union Troops had to jump down into their trenches and then scramble out the other side.
Either which way you care to look at this, the Battle of The Crater was an unmitigated disaster for the Union and turned into what Gen. William Mahone accurately described as a "Turkey Shoot".
On a side note, the Confederate Troops tried something similar a few months later but lacked the tunneling expertise of the Union & had even fewer supplies to carry out the operation.